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Question

Using properties of definite integrals, evaluate:
π20sinxcosx1+sinxcosxdx

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Solution

Let =π/20sinxcosx1+sinxcosxdx
I=π/20sinx1+sinxcosxdxπ/20cosx1+sinxcosxdx
Here a+bx=π2x, so using the property
baf(x)dx=baf(a+bx)dx
I=π/20sin(π2x)1+sin(π2x)cos(π2x)dxπ/20cosx1+sinxcosxdx
I=π/20cosx1+cosxsinxdxπ/20cosx1+sinxcosx
I=0

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